Question

Three different stones $P$, $Q$ and $R$ of different weights are lifted from the ground level to different heights on different planets as given below:
$P$ : A $250g$ stone is lifted to $10m$ on the Earth.
$Q$ : A $800g$ stone is lifted to $2m$ on Saturn.
$R$ : A $1kg$ stone is lifted to $1m$ on Jupiter.
Which of the following statements is true?
(Given that the acceleration due to gravity on the Earth, the Saturn and the Jupiter are $10m{s}^{-2},15m{s}^{-2}$ and $25m{s}^{-2}$ respectively).

• A. More energy is required to lift stone $Q$ than stone $P$
• B. More energy is required to lift stone $P$ than stone $R$
• C. Stone $P$ and stone $Q$ require the same amount of energy
• D. Stone $P$ and stone $R$ require the same amount of energy

Answer 1

The correct option is D Stone $P$ and stone $R$ require the same amount of energy

Work done on P:$W_P=m_P{g}_e{h}_P$ where $g_e$ corresponds to acceleration due to gravity on earth.

$W_P=0.25\times 10\times 10=25J$

Similarly,$W_Q=m_Q{g}_s{h}_Q$

$=0.8\times 15\times 2=24J$

And,$W_R=m_R{g}_j{h}_R=1\times 25\times 1=25J$